Merton Portfolio Optimization Through Optimal Stochastic Control

• Grant number: 25/07615-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2025
• End date: July 31, 2026
• Field of knowledge: Applied Social Sciences - Economics - Quantitative Methods Applied to Economics
• Principal Investigator: Luiz Koodi Hotta
• Grantee: Guilherme Valverde Freiria
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/02538-0 - Time series, wavelets, high dimensional data and applications, AP.TEM

Abstract

Merton's (1971) portfolio optimization problem addresses the investor's decision regarding the optimal allocation of wealth between a risk-free asset and a risky asset, with the objective of maximizing the expected utility of future wealth. This project aims to provide an introduction to stochastic control through the study of the formulation and solution of this classical model, serving as a starting point for understanding the key concepts involved in the theory.To this end, fundamental topics such as the Dynamic Programming Principle (DPP) and the Hamilton-Jacobi-Bellman equation will be explored, as they are central tools in the analysis of optimal control problems. In addition, a review of essential concepts in financial markets and stochastic calculus will be conducted in order to provide the theoretical foundation necessary for understanding and formulating the portfolio optimization problem.Merton's model is widely recognized in the quantitative finance literature and serves as the basis for the formulation and solution of various other financial problems. This work aims to develop both the mathematical understanding and the theoretical intuition behind this fundamental model. (AU)